Lectures on the Structure of Algebraic Groups and Geometric Applications (Cmi Lecture Series in Mathematics) - Hardcover

Brion, Michel; Samue, Preena; Uma, V.

Hardcover

ISBN 10: 9380250460 ISBN 13: 9789380250465

Publisher: Hindustan Book Agency, 2012

Synopsis

This book originates from a series of 10 lectures given by Professor Michel Brion at the Chennai Mathematical Institute during January 2011. The book presents a theorem due to Chevalley on the structure of connected algebraic groups, over algebraically closed fields, as the starting point of various other structure results developed in the recent past. Chevalley's structure theorem states that any connected algebraic group over an algebraically closed field is an extension of an abelian variety by a connected affine algebraic group. This theorem forms the foundation for the classification of anti-affine groups which plays a central role in the development of the structure theory of homogeneous bundles over abelian varieties and for the classification of complete homogeneous varieties. All these results are presented in this book. The book begins with an overview of the results exposed, the proofs of which constitute the rest of the book. Various open questions also have been indicated in the course of the exposition.

This book assumes certain preliminary knowledge of linear algebraic groups, abelian varieties and algebraic geometry. The book is intended for graduate students and researchers in algebraic geometry.

About this title

About the Author

Michel Brion, Institut Fourier, Grenoble, France.

Preena Samue, Chennai Mathematical Institute, Chennai, India.

V. Uma, Indian Institute of Technology Madras, Chennai, India.

Edition details

• Publisher: Hindustan Book Agency
• Publication date: 2012
• Language: English
• ISBN 10: 9380250460
• ISBN 13: 9789380250465
• Binding: Hardcover
• Number of pages: 128